We processed the raw data from the GDx image series to generate images representing the principle optical properties of the returning light
29 33 (Burns SA, et al.
IOVS 2001;42:ARVO Abstract 3808; Mellem-Kairala M, et al.
IOVS 2002;43:ARVO E-Abstract 245). We developed a set of routines in commercial software (MatLab; The Mathworks, Natick, MA) to use with the 20 pairs of raw images (Burns SA, et al.
IOVS 2001;42:ARVO Abstract 3808).
29 For simplicity the analysis assumes that the major factor altering polarization properties in the retina is the linear birefringence of the nerve fiber layer. As the cornea of the eye is also birefringent, we used the average corneal compensation provided by the commercially available GDx, although future work could benefit from the individual compensation recently developed
40 43 (see the Discussion section). The other major factor altering the polarization properties of light in the retina is then assumed to be multiple scattering, which depolarizes light.
27 28 Thus, light returning through the pupil from the retina can be classified along a continuum that depends on how polarized the sampled light is. This can be quantified by separating the light into two components. One component is light that has been specularly reflected, or at most scattered only a few times, and thus retains its polarization. The second component is light that has been multiply scattered and thus has lost its polarization.
Because the retina is birefringent,
34 44 45 separating these components requires the application of polarimetric analysis (Dreher AW, et al.
IOVS 1992;33:ARVO Abstract 968).
30 32 37 38 46 47 48 Although a full description of the polarization properties requires the measurement of sufficient independent conditions to specify all possible parameters of polarization, detailed analyses of partial polarimetry in the eye, such as that performed by the GDx, have been described that allow comparison to the full model.
31 38
Figure 1 shows the difference across images obtained for each of the two detectors of the GDx, for 4 of the 20 input polarization angles. On the left of
Figure 2 is shown one image pair, with a region of interest indicated on the images. On the right, the average grayscale value within this 3 × 3-pixel region of interest is plotted as a function of input polarization. As expected
30 31 the intensity of the pixel varied approximately sinusoidally as the input angle of polarization was rotated. The angle of the retinal birefringence is represented by the phase of this curve. This phase varied with retinal position, because the nerve fiber layer varies in orientation across the retina. The minimum in the crossed detector intensity function represents the angle for which the incoming light is aligned with either the fast or slow axis of the retinal birefringence. At this location the only light that gets to the crossed detector is light that has undergone an alteration of the polarization properties, such as having been depolarized by multiple scattering or otherwise changed in its polarization state. To determine the retinal distribution of the multiple retinal scattering in a system that contains chiefly linear birefringent elements, it is therefore necessary only to find the minimum intensity for each pixel.
The grayscale value of each image in the image series was corrected by using the spatially resolved offset and gain calibrations provided with each instrument. Next, all images were aligned to correct for eye movements. We then calculated image types representing a particular aspect of the reflectance of the retina.
First, we computed the distribution of depolarized light (the depolarized light image), which is the minimum value of light detected for the crossed detector and all input polarization angles.
\[I_{\mathrm{DP}}\ {=}\ \mathrm{min}{[}\mathrm{F}({\alpha}){]}\]
where
I DP is the depolarized light intensity at that pixel, F is the intensity function of the crossed detector for all images in a set, α is the angle of input polarization, and min is the minimum of the function. Note that this value represents the estimate of half the amount of depolarized light returning from the retina at a given location.
Second, we computed the parallel polarized light image as the average intensity for the parallel polarized light minus the depolarized light contribution at each pixel (
I DP).
\[I_{\mathrm{PP}}\ {=}\ ({\Sigma}(\mathrm{PPD}_{\mathrm{i}}))/20\ {-}\ I_{\mathrm{DP}}\]
where
I PP is the parallel polarized light intensity at that pixel, PPD (i = 1,20) is the total intensity for the parallel polarized detector and
I DP is as just described. This value represents the average amount of light that retains its original polarization, independent of input polarization.
Third, we calculated the grand mean of the light returning to both detectors for all input polarization states.
\[I_{\mathrm{M}}\ {=}\ ({\Sigma}(\mathrm{PPD}_{\mathrm{i}}\ {+}\ \mathrm{DPD}_{\mathrm{i}}))/40\]
where
I M is the light intensity at each pixel averaged across images, PPD is the light intensity for the parallel polarized detector, and DPD the intensity distribution for the perpendicularly polarized detector (i = 1,20). This value represents the average relative reflectance of the retina, or conversely the relative reflectance that would be measured with a polarization insensitive detection channel and a randomly polarized light source. This image is what is obtained with a typical confocal SLO.
Finally, for comparison to the GDx output, we calculated the polarization modulation amplitude image, or
I PMA, which represents input polarization dependent change in intensity, as
\[I_{\mathrm{PMA}}\ {=}\ \mathrm{max}{[}\mathrm{F}({\alpha}){]}\ {-}\ \mathrm{min}{[}\mathrm{F}({\alpha}){]}.\]
This image represents, as high-intensity, regions of the retina where the polarization of the returning light is most dependent on the polarization of the illumination light.
For these images, although the intensities vary markedly, with I DP typically being the smallest, the expected proportion of multiply scattered light from most to least is I DP > I M > I PP. All the images to be shown are scaled for visibility of small features in a print format. Thus, the actual intensities, although used in all computations, are not shown in the figures, because I DP is small in comparison to I PP in relatively normal eyes.